If A={1,3,5},how many elements have P(A)?

Answer

To solve the problem of finding the number of elements in the power set P(A) for the set A = {1, 3, 5}, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Set A**:
We are given the set A = {1, 3, 5}.

2. **Count the Elements in Set A**:
Count the number of elements in set A.
- Set A has 3 elements: 1, 3, and 5.

3. **Understand the Concept of Power Set**:
The power set P(A) is the set of all subsets of A, including the empty set and A itself.

4. **Use the Formula for the Number of Subsets**:
The number of elements in the power set of a set with n elements is given by the formula:
\[ |P(A)| = 2^n \]
where n is the number of elements in the set A.

5. **Substitute the Value of n**:
Since A has 3 elements (n = 3), we substitute this value into the formula:
\[ |P(A)| = 2^3 \]

6. **Calculate the Value**:
Now, calculate \(2^3\):
\[ 2^3 = 8 \]

7. **Conclusion**:
Therefore, the number of elements in the power set P(A) is 8.

### Final Answer:
The number of elements in P(A) is 8.

---